How do I convert kg/m3 to g/cm3 and understand the logic behind it?

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SUMMARY

The conversion from kg/m³ to g/cm³ involves understanding the relationship between units of mass and volume. Specifically, 3200 kg/m³ converts to 3.2 g/cm³ by applying dimensional analysis, where 1 kg equals 1000 g and 1 m³ equals 1,000,000 cm³. The confusion arises from the fact that while a cubic meter is larger than a cubic centimeter, the conversion requires division by a million to account for the volume difference. This process ensures that the units are consistent and correctly reflect the density.

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  • Familiarity with metric system prefixes (kilo, centi)
  • Basic algebraic manipulation skills
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Homework Statement




How do I convert kg/m3 to g/cm3?.

3200kg/m^3 ---> 3.2g/cm^3


Homework Equations




The question was 3200kg/m3 = 3.2g/cm3. I don't understand the steps involved?

The Attempt at a Solution



I know how to do dimensional analysis, but I just don't really understand the logic in this. I'll go step by step and please explain this to me it is crucial!


1) 3200kg/m^3 ----> g/cm^3

2) 3200kg/m^3 * 1000kg/1g*1m^3/1*10^-6cm^3 = 3.2kg/cm^3

I just don't understand why I divide g/m^3 by a million to reach g/cm^3. Isnt one cm^3 a smaller value(or area) than a m^3? Shouldn't I be multiplying by a million?

For instance: if I don't have a density and simply convert 100m^3 to 100cm^3 the answer is 100 000 000 cm^3. This makes sense because a metre is larger than a CM thus the value will be bigger .

So, Why is this not the case for when I have a density? Why do I have to divide by a million in order to go from m^3 to cm^3 in that case and ultimately reach a smaller value.

Please help me understand where my logic goes wrong.
 
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3200 kg m-3 = 3200 kg m-3 X 1000 g kg-1/ 100000 cm3 m-3
 
? what
 
Convert kg into g. (multiplying 1000 g per kg)

Convert cubic metre into cubic centimetre (dividing 1000000 cc per cubic metre)

Dimensions are matched, so we get the right answer.
 
The dimensions can match but the coefficiant(value in front) can be in either spot.. so technically can still have the wrong answer..
 
Man, they are correct. If you are adamant to make mistake, even God can't help it then. Using dimensions in coefficients helps us to determine if we are going on the right path.

Ask yourself - How many grams in a kilogram? How many cc in a litre -> how many litres in a cubic metre?
 
yeah- its all about 'ask yourself' - I just don't get why I am dividing by a million if a m^3 is bigger than a metre^3..
 
? What are you saying!? Isn't metre is shorted as m?
 

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